arXiv subjects
Publications and source records attributed to Jawad Abuhlail.
Given a coalgebra $C$ over a commutative ring $R,$ we show that $C$ can be considered as a (not necessarily counital) $C^{\ast op}$-coring. Moreover, we show that this coring has a left (right) counity if and only if $C$ is coseparable as an $R$-coalgebra.
In this note we consider different versions of coinduction functors between categories of comodules for corings induced by a morphism of corings. In particular we introduce a new version of the coinduction functor in the case of locally projective corings as a composition of suitable ``Trace'' and ``Hom'' functors and show how to derive it from a more general coinduction functor between categories of type $σ\lbrack M].$ In special cases (e.g. the corings morphism is part of a morphism of measuring $α$-pairings or the corings have the same base ring), a version of our functor is shown to be isomorphic to the usual coinduction functor obtained by means of the cotensor product. Our results in this note generalize previous results of the author on coinduction functors between categories of comodules for coalgebras over commutative base rings.